Solve ff(x)=5x2-11

$$f f ( x ) = 5 x 2 - 11$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{11-5x_{2}}{f^{2}}\text{, }&f\neq 0\\x\in \mathrm{C}\text{, }&x_{2}=\frac{11}{5}\text{ and }f=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply f and f to get f^{2}.

$$f^{2}x=5x_{2}-11$$

Divide both sides by f^{2}.

$$\frac{f^{2}x}{f^{2}}=\frac{5x_{2}-11}{f^{2}}$$

Dividing by f^{2} undoes the multiplication by f^{2}.

$$x=\frac{5x_{2}-11}{f^{2}}$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{11-5x_{2}}{f^{2}}\text{, }&f\neq 0\\x\in \mathrm{R}\text{, }&x_{2}=\frac{11}{5}\text{ and }f=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply f and f to get f^{2}.

$$f^{2}x=5x_{2}-11$$

Divide both sides by f^{2}.

$$\frac{f^{2}x}{f^{2}}=\frac{5x_{2}-11}{f^{2}}$$

Dividing by f^{2} undoes the multiplication by f^{2}.

$$x=\frac{5x_{2}-11}{f^{2}}$$

Solve for f (complex solution)

$$\left\{\begin{matrix}f=-ix^{-\frac{1}{2}}\sqrt{11-5x_{2}}\text{; }f=ix^{-\frac{1}{2}}\sqrt{11-5x_{2}}\text{, }&x\neq 0\\f\in \mathrm{C}\text{, }&x_{2}=\frac{11}{5}\text{ and }x=0\end{matrix}\right.$$

Solve for f

$$\left\{\begin{matrix}f=\sqrt{\frac{5x_{2}-11}{x}}\text{; }f=-\sqrt{\frac{5x_{2}-11}{x}}\text{, }&\left(x_{2}\geq \frac{11}{5}\text{ and }x>0\right)\text{ or }\left(x_{2}\leq \frac{11}{5}\text{ and }x<0\right)\\f\in \mathrm{R}\text{, }&x_{2}=\frac{11}{5}\text{ and }x=0\end{matrix}\right.$$